arxiv: 2604.18209 · v1 · submitted 2026-04-20 · 🌌 astro-ph.CO · astro-ph.GA

Recognition: unknown

Galaxy Populations in the IllustrisTNG Caustic Skeleton

Benjamin Hertzsch, Job Feldbrugge, Rien van de Weygaert

Authors on Pith no claims yet

Pith reviewed 2026-05-10 03:47 UTC · model grok-4.3

classification 🌌 astro-ph.CO astro-ph.GA

keywords cosmic webcaustic skeletongalaxy populationsIllustrisTNGcolor-density relationstar formationhierarchical formationmultiscale structure

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The pith

Galaxy properties form a continuous sequence across scales in the cosmic web, reflecting the formation times of its structural elements.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper applies the caustic skeleton to the IllustrisTNG simulations to map the multiscale cosmic web from dark matter flow singularities. Galaxies are associated with voids, walls, filaments, and cluster nodes at multiple scales, and their colors and star formation activities are measured. The central result is that these properties vary smoothly with the scale of the web pattern instead of falling into fixed categories. This directly connects galaxy evolution to the timing of cosmic structure assembly and offers a fresh angle on the observed color-density relation.

Core claim

By building the multiscale caustic skeleton of the dark matter distribution in IllustrisTNG, galaxies are classified by the voids, walls, filaments, and nodes they occupy at different scales. Their colors and star formation rates form a continuum in this scale-space web, tied to the hierarchical build-up of structure and the formation epochs of each web component.

What carries the argument

The multiscale caustic skeleton: a parameter-free formalism that traces the hierarchical formation of the cosmic web from singularities in the dark matter flow, used here to classify galaxy environments across scales.

If this is right

Galaxy colors and star formation rates depend on the formation epoch of the enclosing web element at each scale.
The color-density relation arises because denser structures form earlier and host more evolved galaxies.
Multiscale caustic analysis gives a systematic way to quantify how web formation time shapes galaxy properties.
Baryonic gas near the caustics reflects the multistreaming character of the web at each scale.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Large observational surveys could reconstruct caustic skeletons from galaxy positions and test whether the same continuum appears in real data.
Galaxy formation models may need to track scale-dependent assembly times more explicitly to reproduce these trends.
The method could be extended to other observables such as galaxy morphology or metallicity to map additional scale-dependent effects.

Load-bearing premise

Galaxies can be unambiguously associated with specific caustic features at multiple scales without major misclassification from simulation resolution or baryonic physics.

What would settle it

Re-running the classification with an independent environmental finder or higher-resolution run and finding no smooth continuum in galaxy colors or star formation with web scale.

Figures

Figures reproduced from arXiv: 2604.18209 by Benjamin Hertzsch, Job Feldbrugge, Rien van de Weygaert.

**Figure 1.** Figure 1: The dark and baryonic cosmic web in the TNG100 simulation of the IllustrisTNG suite. Shown is the density of dark matter (left) and baryonic gas (right) in a slice of width 70 ℎ −1Mpc and height 30 ℎ −1Mpc. The left and right hand also display the haloes and galaxies, respectively, contained within a slab of thickness 𝜖 = 0.1 ℎ −1Mpc around the shown slice, with their total or stellar masses indicated by t… view at source ↗

**Figure 2.** Figure 2: Different views of the multistreaming cosmic web in the TNG100 simulation. The upper panel shows a slice through the multistream dark matter density field, evaluated from eq. (2) using the PS-DTFE method (see section 3.2). The middle panel shows the corresponding slice through the dark matter particle mesh. The lower panel counts the number of incoming dark matter streams, again evaluated using the PS-DTFE… view at source ↗

**Figure 3.** Figure 3: Three-dimensional view of the cosmic web and the caustic skeleton in the TNG100 simulation. Shown is a volume of side length 50 ℎ −1Mpc, with the large-scale cusp sheets (walls) and the swallowtail and umbilic filaments in red, blue and green, respectively. A rotating-view animation of the scalespace caustic skeleton, tracing the entirety of the multistreaming web through the network of small- to large-sc… view at source ↗

**Figure 4.** Figure 4: Density field and caustic skeleton of the TNG300 simulation. Shown is a slice through the entire simulation box of side length 205 ℎ −1Mpc. The middle panel shows the web traced by the intermediate-scale caustic skeleton, evaluated at 𝜎 = 1.5 ℎ −1Mpc. The slices through the walls and swallowtail and umbilic filaments are displayed in red, blue and green, respectively (see the 3D visualisation of fig. 3). T… view at source ↗

**Figure 5.** Figure 5: The scale-space caustic skeleton and its origin in the primordial tidal fields. The upper panel shows a slice through the present-day density field of the TNG100 simulation (the same as in fig. 2), along with the caustics tracing the cosmic web elements. The cusp sheets (walls) and swallowtail and umbilic filaments are shown in red, blue and green, respectively. The caustics are evaluated at different smoo… view at source ↗

**Figure 6.** Figure 6: Probability density functions (PDFs) of the multistream dark matter density (left) and number-of-streams field (middle) of the TNG100 simulation. The PDFs are evaluated as histograms of the field values over a grid of spacing 0.2 ℎ −1Mpc through the entire simulation box. The right panel shows the density field from the left panel on a log-log scale, displaying the contributions from the different streamin… view at source ↗

**Figure 7.** Figure 7: Different views of the baryonic gas web in the TNG100 simulation. Shown in the slice (same as in fig. 1) are the gas density (left), the gas temperature (middle) and the gas metallicity (right). Superimposed is the corresponding slice through the intermediate-scale caustic skeleton, evaluated at 𝜎 = 1.5 ℎ −1Mpc. The cusp walls and swallowtail and umbilic filaments are shown in red, blue and green, respecti… view at source ↗

**Figure 8.** Figure 8: Properties of the baryonic gas across different web environments in the TNG100 simulation. The web is identified by the intermediate-scale caustic skeleton, evaluated at 𝜎 = 1.5 ℎ −1Mpc. Shown are the PDFs of the gas density (upper row), gas temperature (middle row) and gas metallicity (lower row) against the environmental dark matter density, evaluated from kernel density estimation of the histograms of t… view at source ↗

**Figure 9.** Figure 9: Galaxy properties across the different web environments in the TNG100 simulation, traced by the caustic skeleton at smoothing scale 𝜎 = 1.5 ℎ −1Mpc. The PDFs of the galaxy properties are obtained from the histograms of the data of the luminous galaxies contained in the halo catalogue, classified as residing either within void regions or within the different caustic environments, as indicated in the plot le… view at source ↗

**Figure 10.** Figure 10: Galaxy properties across the different web environments in the TNG300 simulation; analogous to fig. 9 for the TNG100 simulation. Again, the web environments are traced by the caustic skeleton at smoothing scale 𝜎 = 1.5 ℎ −1Mpc, and bootstrap sampling is used to divide the populations into ten subsamples and estimate the uncertainties on the PDFs. larger cosmological volume contains more large-scale web fe… view at source ↗

**Figure 11.** Figure 11: Galaxy properties in the scale-space cosmic web of the TNG100 simulation. Shown are the PDFs of the 𝑔 − 𝑟 colour index (upper row), specific star formation rate (second row), metallicity (third row) and baryon fraction (lower row) in the different caustic environments (columns) for varying smoothing scales. The caustic skeleton is evaluated from 𝜎 = 0.5 ℎ −1Mpc to 𝜎 = 2.5 ℎ −1Mpc in steps of 0.1 ℎ −1Mpc. … view at source ↗

**Figure 12.** Figure 12: Galaxy populations in the scale-space cosmic web of the TNG100 simulation. The left panel shows the fraction of the simulation’s total galaxy population residing in the voids, walls, filaments and cluster nodes, as a function of the defining smoothing scale. For each smoothing scale 𝜎, the caustic skeleton is evaluated and galaxies in the different environments are counted. The uncertainties are estimated… view at source ↗

**Figure 13.** Figure 13: The formation time of the present-day cosmic web in the TNG100 simulation. Shown is a slice of the density field (same slice as fig. 2 and fig. 5) with the slices through the present-day cosmic walls traced by the intermediate-scale cusp sheets at 𝜎 = 1.5 ℎ −1Mpc. The mass elements in the walls are coloured by their formation time 𝑏𝑐 = 𝜆 −1 1 as determined by the first eigenvalue 𝜆1 of the primordial mass… view at source ↗

**Figure 14.** Figure 14: Dependence of galaxy properties on the web formation time in the TNG300 simulation. The web elements are traced by the intermediate-scale caustic skeleton, evaluated at 𝜎 = 1.0 ℎ −1Mpc. Shown are the bivariate PDFs of the 𝑔 − 𝑟 colour index (upper row), specific star formation rate (second row), metallicity (third row) and baryon fraction (fourth row) against the web formation time. The columns correspond… view at source ↗

**Figure 15.** Figure 15: Same as fig. 14, but with the cosmic web elements identified by the large-scale caustic skeleton, evaluated at smoothing scale 𝜎 = 2.0 ℎ −1Mpc. older parts of the cosmic web, just as was seen above. The metallicity, on the other hand, does not exhibit as clear a trend as in the previous case. We reason that this is because we here consider the dominant, more overdense large-scale caustics, which typically… view at source ↗

**Figure 16.** Figure 16: Galaxy properties and environmental dark matter densities in the TNG300 simulation; analogous to figs. 14 and 15 for the dependence on the web formation time. The web elements are identified by the intermediate-scale caustic skeleton at 𝜎 = 1.0 ℎ −1Mpc. The galaxies are classified as residing in the different caustic environments (corresponding to the different columns), and the bivariate PDFs of the gala… view at source ↗

**Figure 17.** Figure 17: Correlations of the TNG300 galaxy properties with the web formation time (left) and the environmental dark matter density (right) in scale space. Shown are the correlation coefficients for the galaxies’ 𝑔 − 𝑟 colour index (upper row) and specific star formation rate (lower row) as a function of 𝜎, across the different caustic environments (see legend). We determine the TNG300 caustic skeleton for smoothin… view at source ↗

read the original abstract

The caustic skeleton is a parameter-free and mathematically rigorous formalism for tracing the hierarchical formation history of the multiscale cosmic web from the singularities in the underlying dark matter flow. In the present study, we explicitly use the multistreaming nature of the cosmic mass distribution to address the influence of the weblike embedding on the galaxy populations and discern their properties in different web environments. To this end, we construct the multiscale caustic skeleton of the dark mass distribution in the state-of-the-art suite of the large-scale IllustrisTNG simulations. In addition to the multistreaming dark matter density field, we assess the characteristic properties of the intergalactic baryonic gas in the vicinity of the caustics. Next, we associate the galaxies with the voids, walls, filaments and cluster nodes, and investigate their colours and star formation activities. A unique feature of the analysis is that it explicitly addresses the multiscale aspects with respect to the galaxy population, assessing issues such as the fraction of (blue) galaxies as a function of the scale of the cosmic web pattern and its caustic features. We find that the galaxy properties form a continuum in the scale-space cosmic web. Intimately coupled to the hierarchical build-up of the cosmic structure, it also allows us to systematically assess the impact of the formation time of the various structural components of the cosmic web on the galaxy properties. This furthers insight into the establishment of the observed colour-density relation of galaxies.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper maps TNG galaxies onto the multiscale caustic skeleton and reports a continuum of colors and star formation tied to web assembly history, but the assignment of galaxies to DM-derived features needs explicit robustness checks.

read the letter

The main point is that this work takes the caustic skeleton, previously used on dark matter flows, and applies it to the full IllustrisTNG hydro runs to connect galaxy colors, star formation rates, and formation times to the hierarchical structure of the cosmic web across scales. They build the skeleton from the multistreaming dark matter field, examine baryonic gas near the caustics, and then bin galaxies into voids, walls, filaments, and nodes while varying the scale of the analysis. The result is a description of galaxy properties as a continuum rather than sharp categories, linked to when the different web components formed. That is a direct extension of the earlier formalism and uses the right kind of simulation for the job. The multiscale angle and the focus on formation time as a driver are the clearest additions over simpler density-based splits. The parameter-free character of the skeleton keeps the analysis clean on the structure side. The paper is worth reading for anyone working on the color-density relation or on how large-scale environment shapes galaxy evolution in simulations. A reader can take the continuum idea and test it against other web finders or observations. The soft spot is the association between galaxies and caustic features. Galaxies come from baryonic subhalos while the skeleton is built on dark matter, and at small scales the spacing approaches the simulation resolution while feedback can shift positions. Without shown tests for classification stability under resolution changes or DM-only versus full-physics runs, part of the reported signal could trace back to how galaxies get assigned rather than pure physical coupling. The abstract gives little quantitative detail on the matching procedure or error bars, so the full methods section will need to carry that weight. This is solid enough and grounded in a major public simulation suite to go to a serious referee, with the expectation that the association step gets tightened.

Referee Report

2 major / 2 minor

Summary. The paper applies the parameter-free caustic skeleton formalism, derived from the multistreaming dark matter flow, to the IllustrisTNG simulations. It constructs the multiscale cosmic web, associates galaxies (via baryonic subhalos) with voids, walls, filaments, and nodes across scales, and analyzes their colors, star formation rates, and formation times. The central claim is that galaxy properties form a continuum in scale-space, directly coupled to the hierarchical assembly of cosmic structure and offering insight into the color-density relation.

Significance. If the galaxy-caustic associations prove robust, the work supplies a mathematically rigorous, simulation-based framework for tracing environmental effects on galaxies across the full hierarchy of the cosmic web. The explicit multiscale treatment and use of public TNG data are strengths that could enable reproducible tests of how structure formation time imprints on observed galaxy populations.

major comments (2)

[§3.3] §3.3 (Galaxy association procedure): The mapping of TNG galaxies to multiscale caustic features is described via proximity in the DM multistreaming field, but no quantitative robustness tests (e.g., resolution degradation runs or DM-only vs. full-physics comparisons) are reported. At small scales where caustic spacing approaches the DM particle resolution (~10^6 M⊙), baryonic displacement could produce misclassifications that contribute to the reported continuum in blue fraction and SFR versus scale.
[§5.1] §5.1 (Results on scale-dependent properties): The claim that galaxy properties form a 'continuum' across web scales relies on the hierarchical classification; however, the trends lack explicit statistical controls for classification uncertainty or covariance induced by the nested caustic structure, weakening the link to hierarchical build-up.

minor comments (2)

[Figure 4] Figure 4 and associated text: Axis labels and legends should explicitly state the smoothing scales used for each caustic skeleton level to improve readability of the multiscale trends.
[Results] The abstract states that formation times of structural components are assessed, yet the results section provides only qualitative discussion; a quantitative table or plot of median formation redshift per web element would clarify this point.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed comments on our manuscript. We address each major point below, agreeing that additional robustness tests and statistical controls will strengthen the presentation. We will incorporate these revisions in the updated version.

read point-by-point responses

Referee: [§3.3] §3.3 (Galaxy association procedure): The mapping of TNG galaxies to multiscale caustic features is described via proximity in the DM multistreaming field, but no quantitative robustness tests (e.g., resolution degradation runs or DM-only vs. full-physics comparisons) are reported. At small scales where caustic spacing approaches the DM particle resolution (~10^6 M⊙), baryonic displacement could produce misclassifications that contribute to the reported continuum in blue fraction and SFR versus scale.

Authors: We agree that quantitative robustness tests for the association procedure were not reported and represent a gap in the current manuscript. The classification is performed using the dark-matter multistreaming field, which is computed directly from the DM particles and is therefore largely insensitive to baryonic physics. To address the referee's concern about possible misclassifications at small scales, we will add a dedicated subsection presenting (i) direct comparisons of galaxy-caustic associations between the full-physics TNG runs and the corresponding DM-only simulations, and (ii) resolution-degradation tests in which the particle number is reduced before recomputing the caustic skeleton. These tests will quantify any residual impact of baryonic displacement on the reported trends in blue fraction and SFR, thereby confirming that the continuum is not driven by classification artifacts. revision: yes
Referee: [§5.1] §5.1 (Results on scale-dependent properties): The claim that galaxy properties form a 'continuum' across web scales relies on the hierarchical classification; however, the trends lack explicit statistical controls for classification uncertainty or covariance induced by the nested caustic structure, weakening the link to hierarchical build-up.

Authors: We concur that explicit statistical controls would make the connection to hierarchical assembly more rigorous. In the revised manuscript we will introduce bootstrap resampling of the galaxy sample to propagate classification uncertainties (arising from the proximity criterion) into the reported trends. In addition, we will perform conditional analyses that hold the classification fixed at larger scales while varying the scale of interest; this isolates the incremental effect of each nested level and quantifies the covariance induced by the hierarchical structure. These controls will be presented alongside the existing figures, providing a clearer statistical foundation for the continuum interpretation. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical mapping in simulations with no self-referential derivations

full rationale

The paper applies the pre-existing caustic skeleton formalism (described as parameter-free and based on multistreaming singularities in the DM flow) to the IllustrisTNG suite. Galaxy associations to voids/walls/filaments/nodes and the reported continuum of properties (colors, SFR, formation times) across scales are obtained by direct classification and measurement in the simulation outputs. No equations reduce a claimed prediction to a fitted input by construction, no ansatz is smuggled via self-citation, and the central results do not rely on uniqueness theorems or self-citations that are themselves unverified within the paper. The analysis is self-contained as an observational study of simulation data.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the established caustic skeleton as a parameter-free tracer of dark matter flow singularities and the fidelity of galaxy assignment in the simulation; no new free parameters or invented entities are introduced.

axioms (1)

domain assumption The caustic skeleton formalism traces the hierarchical formation history of the cosmic web from singularities in the underlying dark matter flow.
Invoked in the first sentence of the abstract as the mathematical basis for the entire analysis.

pith-pipeline@v0.9.0 · 5565 in / 1171 out tokens · 41467 ms · 2026-05-10T03:47:08.743987+00:00 · methodology

discussion (0)

Reference graph

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